Search results for "Exponential function"

Trace identities and almost polynomial growth

2021

In this paper we study algebras with trace and their trace polynomial identities over a field of characteristic 0. We consider two commutative matrix algebras: $D_2$, the algebra of $2\times 2$ diagonal matrices and $C_2$, the algebra of $2 \times 2$ matrices generated by $e_{11}+e_{22}$ and $e_{12}$. We describe all possible traces on these algebras and we study the corresponding trace codimensions. Moreover we characterize the varieties with trace of polynomial growth generated by a finite dimensional algebra. As a consequence, we see that the growth of a variety with trace is either polynomial or exponential.

Non Linear Fitting Methods for Machine Learning

2017

This manuscript presents an analysis of numerical fitting methods used for solving classification problems as discriminant functions in machine learning. Non linear polynomial, exponential, and trigonometric models are mathematically deduced and discussed. Analysis about their pros and cons, and their mathematical modelling are made on what method to chose for what type of highly non linear multi-dimension problems are more suitable to be solved. In this study only deterministic models with analytic solutions are involved, or parameters calculation by numeric methods, which the complete model can subsequently be treated as a theoretical model. Models deduction are summarised and presented a…

Quantum Property Testing for Bounded-Degree Graphs

2011

We study quantum algorithms for testing bipartiteness and expansion of bounded-degree graphs. We give quantum algorithms that solve these problems in time O(N^(1/3)), beating the Omega(sqrt(N)) classical lower bound. For testing expansion, we also prove an Omega(N^(1/4)) quantum query lower bound, thus ruling out the possibility of an exponential quantum speedup. Our quantum algorithms follow from a combination of classical property testing techniques due to Goldreich and Ron, derandomization, and the quantum algorithm for element distinctness. The quantum lower bound is obtained by the polynomial method, using novel algebraic techniques and combinatorial analysis to accommodate the graph s…

Nonabelian Hodge theory in positive characteristic via exponential twisting

2015

Construction of canonical coordinates for exponential Lie groups

2009

Given an exponential Lie group G, we show that the constructions of B. Currey, 1992, go through for a less restrictive choice of the Jordan-Holder basis. Thus we obtain a stratification of g * into G-invariant algebraic subsets, and for each such subset Ω, an explicit cross-section Σ C Ω for coadjoint orbits in Ω, so that each pair (Ω, Σ) behaves predictably under the associated restriction maps on g * . The cross-section mapping σ: Ω → Σ is explicitly shown to be real analytic. The associated Vergne polarizations are not necessarily real even in the nilpotent case, and vary rationally with ∈ Ω. For each Ω, algebras e 0 (Ω) and e 1 (Ω) of polarized and quantizable functions, respectively, a…

Continuous numerical solutions of coupled mixed partial differential systems using Fer's factorization

1999

In this paper continuous numerical solutions expressed in terms of matrix exponentials are constructed to approximate time-dependent systems of the type ut A(t)uxx B(t)u=0; 0 0, u(0;t)=u(p;t)=0; u(x;0)=f(x);06 x6p. After truncation of an exact series solution, the numerical solution is constructed using Fer’s factorization. Given >0 and t0;t1; with 0<t0<t1 and D(t0;t1)=f(x;t); 06x6p; t06t6t1g the error of the approximated solution with respect to the exact series solution is less than uniformly in D(t0;t1). An algorithm is also included. c 1999 Elsevier Science B.V. All rights reserved. AMS classication: 65M15, 34A50, 35C10, 35A50

Rate of Mixing for Equilibrium States in Negative Curvature and Trees

2021

In this survey based on the recent book by the three authors, we recall the Patterson-Sullivan construction of equilibrium states for the geodesic flow on negatively curved orbifolds or tree quotients, and discuss their mixing properties, emphasizing the rate of mixing for (not necessarily compact) tree quotients via coding by countable (not necessarily finite) topological shifts. We give a new construction of numerous nonuniform tree lattices such that the (discrete time) geodesic flow on the tree quotient is exponentially mixing with respect to the maximal entropy measure: we construct examples whose tree quotients have an arbitrary space of ends or an arbitrary (at most exponential) grow…

Application of a radiative cooling model to daily minimum temperature prediction

1985

A model of exponential decrease of temperature is applied to the study of night cooling in an agricultural area of citrus orchards located near the Valentian Coast (Spain). A set of annual average parameters which determine that cooling is obtained by using temperature measurements at different levels during two years. These parameters appear to be representative of the thermal behaviour of the area of study. The attainment of such parameters allows a prediction of the minimum temperatures of the area to an accuracy of £1.5 K, knowing the temperature at sunset and some time later.

A Check of Water Drop Impact Effects on Surface Soil Saturated Hydraulic Conductivity

2020

The post-tillage dynamics of the surface soil saturated hydraulic conductivity, Ks, was studied at the Masse experimental station (central Italy, silty-clay-loam soil). A sequence of experiments was performed by rainfall simulation on two replicated micro-plots (width 1 m, length 0.92 m, slope 16%) established on bare soil. Each high-intensity rainfall simulation was preceded by a low-intensity wetting phase. The soil water content, w, was measured before wetting and both before and after simulation. Runoff was measured at 5 min intervals. The infiltration rate was calculated as the difference between rainfall intensity and runoff rate. Finally, Ks was assumed to be equal to the infiltratio…

Fractional model of concrete hereditary viscoelastic behaviour

2016

The evaluation of creep effects in concrete structures is addressed in the literature using different predictive models, supplied by specific codes, and applying the concepts of linear viscoelastic theory with ageing. The expressions used in the literature are mainly based on exponential laws, which are introduced in the integral expression of the Boltzmann principle; this approach leads to the need of finding approximated numerical solutions of the viscoelastic response. In this study, the hereditary fractional viscoelastic model is applied to concrete elements, underlining the convenience of using creep or relaxation functions expressed by power laws. The full reciprocal character of cree…